Given an input image, a prior heatmap-based method [1]} estimates three 1D heatmaps \(H=\lbrace H^x, H^y, H^z\rbrace \)  for each human joint and mesh vertex.
The x and y-axis heatmaps \(H^x, H^y\)  are defined in the image space, and the z-axis heatmaps \(H^z\)  are defined in the depth space relative to root joint.
We denote the joint heatmaps as \(H_J \in \mathbb {R}^{N_J \times D \times 3}\)  and vertex heatmaps as \(H_V \in \mathbb {R}^{N_V \times D \times 3}\) , where \(N_J\)  is the number of joints, \(N_V\)  is the number of vertices, and \(D\)  is the heatmap resolution.
The heatmaps are predicted based on image features \(F \in \mathbb {R}^{c \times h \times w}\)  extracted by a backbone network as follows:
\(\begin{split}H^x &= f^{\text{ 1D},x} (\text{avg}^y (f^\text{ up} (F))), \\H^y &= f^{\text{ 1D},y} (\text{avg}^x (f^\text{ up} (F))), \\H^z &= f^{\text{ 1D},z} (\psi (\text{avg}^{x,y} (F)))),\end{split}\) 
